Some limit distributions for processes with independent increments.

Let $\xi(t)$ ($t\ge 0$; $\xi(0)=y_0>0$) be a homogeneous continuous from the left and from below process with independent increments. Put $\displaystyle\eta=\sup\{t\colon\inf_{0\le s\le t}\xi(s)>0\}$.
This paper considers the limit distribution $\mathbf P\{\xi(t)<x\mid\eta>t\}$, $t\to\infty$.